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To: Richnorth who wrote (86553)	6/6/2002 5:23:41 PM
From: E. Charters	Read Replies (1) \| Respond to of 116832

A second year student could work out trajectories in a vacuum, that is an integration of a tangent equation. But let's add, differential velocity due to air resistance, deviation due to precession due to spin of projectile and its decay, coriolis force due to the spinning of the earth under the missile, differential air resistance due to height, differential gravity due to height for long range missiles and you have an interesting differential equation. Professors of mine told me not to expect a snap answer. Work of Legendre: From 1775 to 1780 he taught with Laplace at Ecole Militaire where his appointment was made on the advice of d'Alembert. He then decided to enter for the 1782 prize on projectiles offered by the Berlin Academy. The actual task was stated as follows:- Determine the curve described by cannonballs and bombs, taking into consideration the resistance of the air; give rules for obtaining the ranges corresponding to different initial velocities and to different angles of projection. His essay Recherches sur la trajectoire des projectiles dans les milieux résistants won the prize and launched Legendre on his research career. In 1782 Lagrange was Director of Mathematics at the Academy in Berlin and this brought Legendre to his attention. He wrote to Laplace asking for more information about the prize winning young mathematician. EC<:-}